Precalculus Examples

$\log (9) \cdot (5 \sqrt{81})$

Step 1

Rewrite $81$ as $9^{2}$ .

$\log (9) \cdot (5 \sqrt{9^{2}})$

Step 2

Pull terms out from under the radical, assuming positive real numbers.

$\log (9) \cdot (5 \cdot 9)$

Step 3

Multiply $5$ by $9$ .

$\log (9) \cdot 45$

Step 4

Multiply $\log (9) \cdot 45$ .

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Step 4.1

Reorder $\log (9)$ and $45$ .

$45 \cdot \log (9)$

Step 4.2

Simplify $45 \cdot \log (9)$ by moving $45$ inside the logarithm.

$\log (9^{45})$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\log (9^{45})$

Decimal Form:

$42.94091292 \dots$